When exporting a .obj or .fbx how do you keep the color/texture?
Unwrap your model, create new material and assign a jpg texture to it (or create new in in Blender's UV/Image editor and paint it in Texture Paint mode).

Export the model to FBX.
Open Roblox Studio, create MeshPart object and import the FBX using the Open Mesh File button


Texture should be assigned automatically



If you want to use simple colors instead of textures, you can use Vertex Paint mode and color your model using this method. Roblox can import vertex colors contained in your model (if not, make sure you have ticked export vertex colors in the FBX/OBJ exporter dialog in Blender).